Exponents Worksheet & Practice © 2007 mathwarehouse.com Overview This exponents worksheet focuses on two of the main rules for exponents and asks students to apply both of these rules (see below) to various types of problems. xa • xb = xa+b i.e. (xa )b = xa•b Exponent rule 1: multiplying exponents i.e. Exponent rule 2:exponents of exponents Questions range in difficulty and the concluding questions include higher level thinking about the rules of exponents in math. © 2007 www.mathwarehouse.com All Rights Reserved Commercial Use Prohibited TEACHERS: Feel free to make copies of this worksheet for the sole purpose of use in your own classroom. ENJOY!!! Redistribution in any other form is prohibited. More worksheets and activities available at www.mathwarehouse.com/classroom/worksheets-and-activities.php Exponents worksheet on next page Exponents Worksheet I. Directions: Rewrite the each question below without the exponents and simplify. 1) 2 2 • 2 3 = 2) 2 2 • 2 4 = 3) 2 2 • 2 5 = 4) 2 2 • 26 = 5) 2 3 • 2 5 = 6) 3 2 • 3 3 = 7) x • x = 2 3 From Numbers to letters! 9) x12 • x 3 = 8) x 4 • x 3 = 10) x 6 • x 20 = GENERAL SUMMARY: Fill in the blank: xa • xb = xa__b Part II Directions: 11) (x)2 = __• __ 16) (x 2 )3 = 12) (2 2 )2 = 17) (x 5 )2 = 13) (2 2 )3 = 18) (x 3 )4 = 14) (2 2 )4 = 19) (x 5 )4 = 15) (32 )3 = 20) (x10 )4 = (x ) = x a b a __ b GENERAL SUMMARY: Fill in the blank: Putting It all Together! III. Simplify: 21) x 2 • (x 2 )3 = 24) z 3 • (z11 )5 = 22) x 3 • (x 5 )2 = 25) Find the product of (z 3 )2 and (z 3 )4 23) z12 • (z 6 )5 = 26) z 2 • (z 3 )0 = Determine what number could replace the question mark Example: (x10 )2 = x17 • x? Example2: (x12 )3 = x29 • x? 27) (x2 )3 = x2 • x? 31) (x3 )? = x5 • x7 28) (x3 )2 = x5 • x? 32) (x4 )? = x5 • x11 29) (x5 )2 = x3 • x? 33) (x? )3 = x2 • x10 30) (x2 )? = x4 • x22 34) (x? )2 = x5 • x20 35) How many different pairs of integers could replace the question marks below? (x? )? = x2 • x6 Think-Pair-Share Mr. Morris gave the class a problem that was very similar to the questions above (27— 34) so the students were asked to find a number that could replace the question mark. The problem was: (x3 )0 = x5 • x? . Jennifer says that the question mark should be replaced by 0. John says that the question mark should be 1. Joseph says that the question mark should be –5. Mary says that the question is impossible to answer.. Who is correct? Explain why: Explanation: 36) Is the following statement true? (xa )b = (x b )a Why or why not? © 2007 mathwarehouse.com Extension Directions: Determine the value of a in the equations below. 1) (xa )6 = x2 • x10 2) (xa +1 )5 = x2 • x13 3) (xa + 4 )2 = x12 • x4 4) (xa + 2 )3 = x9 • x6 5) (xa )2 = xa • x1 6) (xa + 4 )3 = xa • x14 7) (xa +7 )2 = x5a • x5 8) (xa +7 )0 = x5a © 2007 mathwarehouse.com © 2007 www.mathwarehouse.com All Rights Reserved Commercial Use Prohibited TEACHERS: Feel free to make copies of this worksheet for the sole purpose of use in your own classroom. ENJOY!!! Redistribution in any other form is prohibited. More worksheets and activities available at www.mathwarehouse.com/classroom/worksheets-and-activities.php